Presentation on theme: "Control and Feedback Introduction Open-loop and Closed-loop Systems"— Presentation transcript:
1 Control and Feedback Introduction Open-loop and Closed-loop Systems Chapter 7Control and FeedbackIntroductionOpen-loop and Closed-loop SystemsAutomatic Control SystemsFeedback SystemsNegative FeedbackThe Effects of Negative FeedbackNegative Feedback – A Summary
2 7.1IntroductionEarlier we identified control as one of the basic functions performed by many systemsoften involves regulation or commandInvariably, the goal is to determine the value or state of some physical quantityand often to maintain it at that value, despite variations in the system or the environment
3 Open-loop and Closed-loop Systems 7.2Open-loop and Closed-loop SystemsSimple control is often open-loopuser has a goal and selects an input to a system to try to achieve this
4 More sophisticated arrangements are closed-loop user inputs the goal to the system
5 Automatic Control Systems 7.3Automatic Control SystemsExamples of automatic control systems:temperature control using a room heater
6 Examples of automatic control systems: Cruise control in a car
7 Examples of automatic control systems: Position control in a human limb
8 Examples of automatic control systems: Level control in a dam
9 7.4Feedback SystemsA generalised feedback system
10 By inspection of diagram we can add values or rearranging
11 This the transfer function of the arrangement Terminology: ThusThis the transfer function of the arrangementTerminology:A is also known as the open-loop gainG is the overall or closed-loop gain
12 Effects of the product AB If AB is negativeIf AB is negative and less than 1, (1 + AB) < 1In this situation G > A and we have positive feedbackIf AB is positiveIf AB is positive then (1 + AB) > 1In this situation G < A and we have negative feedbackIf AB is positive and AB >>1- gain is independent of the gain of the forward path A
13 Negative Feedback Negative feedback can be applied in many ways 7.5Negative FeedbackNegative feedback can be applied in many waysXi and Xo could be temperatures, pressures, etc.here we are mainly interested in voltages and currentsParticularly important in overcoming variabilityall active devices suffer from variabilitytheir gain and other characteristics vary with temperature and between deviceswe noted above that using negative feedback we can produce an arrangement where the gain is independent of the gain of the forward paththis gives us a way of overcoming problems of variability
14 Consider the following example (Example 7.1 in text) We will base our design on our standard feedback arrangementExample: Design an arrangement with a stable voltage gain of 100 using a high-gain active amplifier. Determine the effect on the overall gain of the circuit if the voltage gain of the active amplifier varies from 100,000 to 200,000.
15 We will use our active amplifier for A and a stable feedback arrangement for B Since we require an overall gain of 100so we will use B = 1/100 or 0.01
16 Now consider the gain of the circuit when the gain of the active amplifier A is 100,000
17 Now consider the gain of the circuit when the gain of the active amplifier A is 200,000
18 However, it does require that B is stable Note that a change in the gain of the active amplifier of 100% causes a change in the overall gain of just 0.05 %Thus the use of negative feedback makes the gain largely independent of the gain of the active amplifierHowever, it does require that B is stablefortunately, B can be based on stable passive components
19 Implementing the passive feedback path to get an overall gain of greater than 1 requires a feedback gain B of less than 1in the previous example the value of B is 0.01this can be achieved using a simple potential divider
20 Thus we can implement our feedback arrangement using an active amplifier and a passive feedback network to produce a stable amplifierThe arrangement on the right has a gain of 100 …… but how do we implement the subtractor?
21 A differential amplifier is effectively an active amplifier combined with a subtractor. A common form is the operational amplifier or op-ampThe arrangement on the right has a gain of 100.
22 In this circuit the gain is determined by the passive components and we do not need to know the gain of the op-amphowever, earlier we assumed that AB >> 1that is, that A >> 1/Bthat is, open-loop gain >> closed-loop gaintherefore, the gain of the circuit must be much less than the gain of the op-ampsee Example 7.2 in the course text
23 The Effects of Negative Feedback 7.6The Effects of Negative FeedbackEffects on Gainnegative feedback produces a gain given bythere, feedback reduces the gain by a factor of 1 + ABthis is the price we pay for the beneficial effects of negative feedback
24 Effects on frequency response from earlier lectures we know that all amplifiers have a limited frequency response and bandwidthwith feedback we make the overall gain largely independent of the gain of the active amplifierthis has the effect of increasing the bandwidth, since the gain of the feedback amplifier remains constant as the gain of the active amplifier fallshowever, when the open-loop gain is no longer much greater than the closed-loop gain the overall gain falls
25 therefore the bandwidth increases as the gain is reduced with feedback in some cases the gain x bandwidth = constant
26 Effects on input and output resistance negative feedback can either increase or decrease the input or output resistance depending on how it is used.if the output voltage is fed back this tends to make the output voltage more stable by decreasing the output resistanceif the output current is fed back this tends to make the output current more stable by increasing the output resistanceif a voltage related to the output is subtracted from the input voltage this increases the input resistanceif a current related to the output is subtracted from the input current this decreases the input resistancethe factor by which the resistance changes is (1 + AB)we will apply this to op-amps in a later lecture
27 Effects on distortion and noise many forms of distortion are caused by a non-linear amplitude responsethat is, the gain varies with the amplitude of the signalsince feedback tends to stabilise the gain it also tends to reduce distortion - often by a factor of (1 + AB)noise produced within an amplifier is also reduced by negative feedback – again by a factor of (1 + AB)note that noise already corrupting the input signal is not reduced in this way – this is amplified along with the signal
28 Negative Feedback – A Summary 7.7Negative Feedback – A SummaryAll negative feedback systems share some propertiesThey tend to maintain their output independent of variations in the forward path or in the environmentThey require a forward path gain that is greater than that which would be necessary to achieve the required output in the absence of feedbackThe overall behaviour of the system is determined by the nature of the feedback pathUnfortunately, negative feedback does have implications for the stability of circuits – this is discussed in later lectures
29 Key Points Feedback is used in almost all automatic control systems Feedback can be either negative or positiveIf the gain of the forward path is A, the gain of the feedback path is B and the feedback is subtracted from the input thenIf AB is positive and much greater than 1, then G 1/BNegative feedback can be used to overcome problems of variability within active amplifiersNegative feedback can be used to increase bandwidth, and to improve other circuit characteristics.